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We consider a general collection of function classes on the interval [ 0 , 1 ] [0,1] defined in terms of certain averages and show that monotone rearrangement does not increase the class constant in each case. The formulation includes B M O BMO and A 2 A_2 with a special choice of the norm and, respectively, characteristic.
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Abdrakhmanov et al. (2024) studied this question.
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